Direction & Distance
🔒 Log in to trackmedium importance~1-2 Q in Tier 16 formulas⚡ 5 shortcuts4 subtopics
Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.
Direction conventions and displacement
Shortest distance
d = \sqrt{x^2 + y^2}
x = net east-west movement, y = net north-south movement.
Triple shortcut
3\text{-}4\text{-}5 \times k
Legs (3k, 4k) give distance 5k: check 6-8-10, 9-12-15, 12-16-20.
Turn directions
\text{left/right} = \text{facing}\pm90^\circ
Left/right are relative to current facing; about-turn is 180°.
Direction faced and net direction
Clockwise cycle
N \to E \to S \to W \to N
Every right turn moves one step along this cycle.
Anticlockwise cycle
N \to W \to S \to E \to N
Every left turn moves one step along this cycle.
Sign reading
(x>0,y>0) \Rightarrow NE
Signs of the net components give the quadrant.